Let $V_i$ be a sequence of $k$ dimensional analytic subsets in $\mathbb C^N$. Suppose that the volume of $V_i$ is uniformly bounded, then Bishop's compactness theorem says that $V_i$ will convergence by sequence to an analytic subsets $V$.
Q1: What is the precise meaning of "converge" here. Q2: Is it possible that a sequence of singular point $q_i\in V_i$ converge to a smooth point $q\in V$. It seems impossible.